Question: Simplify the following expression: $ z = \dfrac{-6n + 2}{n - 5} + \dfrac{3}{8} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{-6n + 2}{n - 5} \times \dfrac{8}{8} = \dfrac{-48n + 16}{8n - 40} $ Multiply the second expression by $\dfrac{n - 5}{n - 5}$ $ \dfrac{3}{8} \times \dfrac{n - 5}{n - 5} = \dfrac{3n - 15}{8n - 40} $ Therefore $ z = \dfrac{-48n + 16}{8n - 40} + \dfrac{3n - 15}{8n - 40} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-48n + 16 + 3n - 15}{8n - 40} $ $z = \dfrac{-45n + 1}{8n - 40}$